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The folks over at PhoneArena created a cool comparison video to show off the capabilities of the Nexus 5 Optical Image Stabilization video camera capabilities. They basically filmed the same scene using the Nexus 4 (which doesn't have OIS) and the Nexus 5 (which does). Despite the obvious smoother image quality of the Nexus 5, it's interesting to note that the picture on the Nexus 5 is a bit darker and is perhaps more "true-to-life." The color is richer on the Nexus 5 and the image on the nexus 4 seems overly bright.

It's also interesting to note that the OIS on the Nexus 5 is not as advanced as it could be. For example, it only uses a 2-axis stabilization function, versus the 3-axis stabilization found in the Nokia Lumia 920. Here's a quote with the full description of the OIS in the Nexus 5 and how it compares to other competing standards,

Now, it’s time to take a deeper look at one specific improvement the Nexus 5 brings and that’s optical image stabilization.

To stabilize videos and images, the Nexus 5 features an InvenSense IDG-2020 dual axis gyroscope. To better understand what this means we have to turn to the way OIS works and what do these axes mean. Basically, optical image stabilization is a physical mechanism that counters movement either on a single lens or on the whole camera body with the latter of course being more efficient. We have 2-axis and 3-axis OIS systems, and the three axes refer to rotational movement. These axes are roll, pitch and yaw (x, y and z). Roll refers to rotation about the longitudinal axis, pitch - to movement about the lateral axis, and yaw about rotation about the vertical axis. The illustration here explains that.

Now, the InvenSense IDG-2020 optical image stabilization unit on the Nexus 5 only stabilizes on 2 axes - roll and pitch, or x and y. This is similar to OIS on the HTC One that’s also 2-axis. Nokia, the company that first started using OIS in smartphones with the Lumia 920, though, uses a more efficient 3-axis stabilization. Moreover, the physical mechanism engulfs the whole optical stack on Lumia smartphones like the 1020, and unlike the single-lens stabilization on the HTC One.